This quantity is dedicated to a number of vital new principles coming up within the functions of Lie teams and Lie algebras to Schrödinger operators and linked quantum mechanical structures. In those purposes, the crowd doesn't seem as a ordinary symmetry staff, yet fairly as a "hidden" symmetry team whose illustration concept can nonetheless be hired to research at least a part of the spectrum of the operator. In mild of the quick advancements during this topic, a distinct consultation used to be equipped on the AMS assembly at Southwest Missouri country collage in March 1992 in an effort to assemble, possibly for the 1st time, mathematicians and physicists operating in heavily comparable components. The contributions to this quantity disguise Lie team tools, Lie algebras and Lie algebra cohomology, illustration thought, orthogonal polynomials, $q$-series, conformal box thought, quantum teams, scattering thought, classical invariant concept, and different themes. This quantity, which includes a superb stability of analysis and survey papers, provides a glance at a few of the present advancements during this terribly wealthy and bright sector.
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